Question

This is the last question I need help with​

Answer 1

Explanation:

So this prism has the triangles faces at the base and top, but the sides are all rectangles, let me know if you can't quite picture that.

Anyway, the surface area will be the sum of all the faces. There are five total, and two of them are the same. The base ad top are the exact same right triangle, so we'll take care of those. each of those faces has an area of .5*4*3 = 6. And since there are two we knw they contribute 12 together. This means that total surface area number 126 has 12 from the base face and the top face, so we can subtract that.

126-12=114

So now we know the three side faces all add up to 114 in^2 for their area. or in other words F1 + F2 + F3 = 114. SO face one plus face two plus face three. Now how do we find the area of the faces?

The side faces have the same height to them, which is the height of the prism, which is what we're looking for. We also know the base length of each of the prisms. Basically each one has a base length of one of the sides of the triangle at the base and top. And how do we find the area of a rectangle? b *h. So fow the Fs become b1*h b2*h and b3 times height, but we know what the bases are.

F1 + F2 + F3 = 114

b1 * h + b2 * h + b3 * h = 114

3h + 4h + 5h = 114

Now we just combine like terms and it's a simple algebraic equation.

12h = 114

h = 9.5

Again, let me know if there's something you don't understand.

Answer 2

Check the picture below.

the triangular prism is really just 2 triangles and 3 rectangles, now, we can get is surface area by simply getting the area of those triangles and rectangles.

looking at the picture, let's notice, the triangles have a base of 4, height of 3.

the rectangles have an area of 3*h, 4*h and 5*h respectively.

and we know the surface area is 126, so then

`\bf \stackrel{\textit{two triangles}}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~\left[ \cfrac{1}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}(4)(3) \right]}+\stackrel{\textit{three rectangles}}{3h+4h+5h}~~=~~\stackrel{\textit{surface area}}{126} \\\\\\ 12+12h=126\implies 12h=114\implies h=\cfrac{114}{12}\implies h=\cfrac{19}{2}\implies h=9.5`